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Theorem fv2 5723
Description: Alternate definition of function value. Definition 10.11 of [Quine] p. 68. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) (Revised by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
fv2  |-  ( F `
 A )  = 
U. { x  | 
A. y ( A F y  <->  y  =  x ) }
Distinct variable groups:    x, y, A    x, F, y

Proof of Theorem fv2
StepHypRef Expression
1 df-fv 5462 . 2  |-  ( F `
 A )  =  ( iota y A F y )
2 dfiota2 5419 . 2  |-  ( iota y A F y )  =  U. {
x  |  A. y
( A F y  <-> 
y  =  x ) }
31, 2eqtri 2456 1  |-  ( F `
 A )  = 
U. { x  | 
A. y ( A F y  <->  y  =  x ) }
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1549    = wceq 1652   {cab 2422   U.cuni 4015   class class class wbr 4212   iotacio 5416   ` cfv 5454
This theorem is referenced by:  elfv  5726
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-sn 3820  df-uni 4016  df-iota 5418  df-fv 5462
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